YABU
I would say that your DH should have consulted you re any plans for his DS to move, it;s not fair that he didn’t. I think it would be fair for you to point that out to him and ask him to be more considerate. But perhaps he took it as a given that his son is welcome in his home if needed. Which is not an unreasonable premise to make.
Is your 4 year old your DH’s child? If not, how would you feel if your DH decided your child was out the door, never to return, the day he or she turns 18 years old? If your 4 years old is yours and DH’s child, are you expecting them to move out when they are 18 year old, come what may? If the answer to those questions is that you would be happy if your DH made your DC move out when they were 18 years old, no matter what the circumstances, then YANBU on that front.
I think it’s sad that your resent the fact that your DH has a close relationship with his son. If your DSS was actually your son I would imagine you would be thrilled, wouldn’t you? If so, then I think you should have a think about what that says about your feelings towards your DSS. You say you are fond of him but I can’t quite reconcile that with your attitude towards his relationship with his father and your territorial feelings around your family home.
When you decided to marry a man with a child, you accepted all that comes with that. Including the possibility that at some point your DH’s child could have to come and live with you. You feel so very territorial about your home (though surely when you married your DH and he moved in that house became YOUR JOINT family home, not just yours?) that I can’t see how you would ever have been happy with that. So I think YABU on that front.
I think YABU to refer to the house you live in with your family as solely yours and not DH’s. I understand that it is your family home and you inherited it, so feel very attached. However, when you marry someone and become a family, it ceases to be solely yours (morally and legally- unless you have enforceable prenup). Would you have sold that house to buy a house jointly with your DH/ or let that house and use your joint incomes to finance a mortgage? Given how you feel about your house, I doubt it.
You need to let your DH know how you feel if you really cannot face having your DSS living with you- do so now so your DSS can be clear about his finances and accomodation options (or lack thereof) prior to finalising university applications. He may not be able to afford student accommodation in London (and I know some universities will not prioritise student halls if a parent lives in London, so it may not even be a case of not being able to afford it) and so needs to know before he applies.